This invention relates generally to optical sensing systems and, more particularly, to a low resolution, very wide angle optical sensing system having a lens in the form of a sphere for use in a missile warning system (MWS). This concept may be used for systems operating in the ultraviolet, visible light, or infrared wavelengths. As in any optical system, the material used to make the lens is selected to be transmitting over the operating spectral region of the system. Materials suitable for making ultraviolet, visible light, or infrared lenses are well known to those skilled in the art.
Prior art devices using a sphere as a lens have been generally thought to have resolution too low to be useful for target recognition systems. The invention, for the first time, utilizes and enhances the properties of such a system and overcomes previous deficiencies in the prior art to make a lens-sphere system which can be successfully used to recognize certain targets.
The effective entrance aperture of a lens-sphere optical system is the diameter of the sphere. However, as shown in FIG. 2, incident rays over this full aperture are not all brought to a common focus. In general, radially symmetric systems have nonvarying imaging quality over a wide field-of-view (FOV), but suffer from a relatively large "blur circle" which may be a handicap in a tactical environment.
Ray tracing analysis shows that, in known systems, the diameter of the blur circle at best focus, in the case when all of the incident rays are considered, is about 20 degrees. If a best position is found for only the central rays (.theta.=0-50 degrees, where .theta. is the angle of incidence at the sphere as illustrated in FIG. 2), then the blur circle diameter is only about 2.9 degrees, which would be considered excellent resolution for certain target recognition systems such as an MWS. However, at this particular focus position for the central rays, the peripheral rays (.theta.=50 to 90 degrees) are spread out over a blur circle diameter of about 58 degrees. Although 60% of the incident energy is contained in the well-focussed central beam, an appreciable fraction (about 40%) of the energy is in the badly defocussed peripheral beam.
The present invention recognizes that if the peripheral rays could be cut out--for example with an aperture stop--then only the relatively well-focussed central rays would be left. However, placing a physical stop in the system destroys the spherical symmetry of the system and defeats the design feature that allows the lens-sphere system to provide uniform performance over a very wide angular range.
To a certain extent, the peripheral rays are naturally obstructed because the transmission, from air into the sphere, decreases with increasing angle of incidence. See Table 1. This beneficial factor was not considered in calculating the percentage of energy in the badly defocused peripheral beam. The extreme peripheral rays which are the most severely defocussed are, very conveniently, the rays most strongly attenuated by this factor.
Additionally, in accordance with one embodiment of the invention, those parts of the surface of the sphere that accept incident rays may be coated with an interference filter specifically designed to attenuate transmission at incident angles over a range such as 60 to 80 degrees. Materials for forming multilayer interference filters are well known. The particular choice of material depends upon the wavelength of intended application and other factors typically considered in such designs. FIG. 3 shows the transmission of a typical angle-dependent filter versus wavelength for on-axis rays and for rays 50.degree. off-axis. This provides additional blocking of those incident rays that contribute only to the blur, and not the central focus spot. FIG. 4 shows the transmission of the angle-dependent filter as a function of angle of incidence.
The invention further demonstrates that even if 100% transmission is assumed at the glass-air boundary for all angles of incidence, the practical impact of the apparently severe defocussing effect of the peripheral rays is very much less than had been previously thought and that, accordingly, the lens-sphere optics appear to be suitable for a spatial MWS.
Table 2 shows the blur circle size as a function of how much of the incident beam is accepted for the case when the focal plane is set to optimally focus the central rays (.theta.=0-50 degrees). The percentage of the available input energy over the full aperture, assuming 100% transmission, is also shown. For example, Table 2 shows that about 58.6% of the input energy is focused within a 2.87 degree radius blur circle, and that the balance (about 41.4%) is spread from a 2.876 degree blur radius to 28.9 degree blur radius. At first sight, it appears that because so large a fraction (41.4%) of the incident radiation is so badly defocussed, the resolution performance is unacceptable.
However, in the MWS application, there is no general background clutter. The targets are, essentially, point-targets and the only factor limiting detection is shot-noise-in-signal. The invention recognizes for the first time that under these conditions, it is not the total energy in the blur circle that is the relevant limitation, but rather the energy density in the blur image as shown in Table 3. Because the blur circle is so large (e.g., 28.9 degree radius), the density (as measured in photons/second/resolution element) is correspondingly very low.
The ability to discriminate two closely spaced targets, with no background signal, depends upon the magnitude of d as shown in FIG. 5(a). FIG. 5(b) illustrates that d depends, in turn, only upon a,b - the point source intensity response function at peak, and one pixel away. All of the energy in the rest of the blur pattern has no effect. It is only when a general background (e.g., cloud clutter) is present that the total energy of the blur is significant.
The low energy density in the out-focus part of the point source intensity response function for the lens-sphere optical system is quantified in Table 3. It presents the same results as Table 2 except that instead of percent energy, the energy density (ED) is given with, and without, the use of the angle-dependent interference filter. For computational simplicity, the energy density for the central rays (up to a 2.82 degree blur circle) is computed as an average over that area. The energy density in the periphery of the blur is calculated for each step. It can be seen that because the area of the peripheral blur is so large, the corresponding energy density is low. Then, as illustrated in FIG. 5, it has very little impact upon the detection and location of point targets against a zero background. The resolution performance of the sensor system depends therefore mainly upon the size of the central spot, and not on the defocus blur caused by the rays coming from the edge of the entrance aperture. Table 3 also illustrates how the intensity of the peripheral (i.e. out-of-focus) component is reduced by the use of the interference filter. This feature is particularly important for discriminating the true target in the presence of a much more intense disturbing source, such as a counter-measure flare.
For example, Table 3 indicates that a source 12.5.degree. away from the target would contribute a signal at the target of 0.01 relative units as compared to 287 relative units from the target. Thus, the disturbing source could be as much as 28,700 times the target intensity before its contribution at the target position equaled that of the target.
TABLE 1 ______________________________________ TRANSMISSION INTO SPHERE AS A FUNCTION OF ANGLE OF INCIDENCE Index = 1.7 ANGLE OF TRANSMISSION INCIDENCE REFRACTION FACTOR ______________________________________ 50 26.78311 .9129376 52 27.6155 .9084619 54 28.41747 .9030868 56 29.1875 .8966404 58 29.92407 .8889159 60 30.62565 .8796649 62 31.29073 .8685876 64 31.91782 .8553212 66 32.50544 .839424 68 33.05216 .8203564 70 33.5566 .7974554 72 34.01742 .7699006 74 34.4334 .7366708 76 34.8034 .6964832 78 35.12631 .647714 80 35.40123 .588285 82 35.62732 .5155074 84 35.8039 .4258591 86 35.93042 .3146587 88 36.00649 .1755941 90 36.03187 -7.152558E-07 ______________________________________
TABLE 2 __________________________________________________________________________ TOTAL ENERGY INPUT HALF ANGLE: 50 DEGS; F LENGTH: 1.2157 BLUR HALF ANGLE: 1.46805 DEGS; __________________________________________________________________________ BLUR AT HALF-THETA = 5 IS .35565% ENERGY = .759613% BLUR AT HALF-THETA = 10 IS .682195% ENERGY = 3.01537% BLUR AT HALF-THETA = 15 IS .950347% ENERGY = 6.69873% BLUR AT HALF-THETA = 20 IS 1.13033% ENERGY = 11.6978% BLUR AT HALF-THETA = 25 IS 1.19164% ENERGY = 17.8606% BLUR AT HALF-THETA = 30 IS 1.10255% ENERGY = 25.% BLUR AT HALF-THETA = 35 IS .829657% ENERGY = 32.899% BLUR AT HALF-THETA = 40 IS .337122% ENERGY = 41.3176% BLUR AT HALF-THETA = 45 IS .414229% ENERGY = 50.% BLUR AT HALF-THETA = 50 IS 1.46805% ENERGY = 58.6824% BLUR AT HALF-THETA = 55 IS 2.87389% ENERGY = 67.101% BLUR AT HALF-THETA = 60 IS 4.68899% ENERGY = 75.% BLUR AT HALF-THETA = 65 IS 6.98036% ENERGY = 82.1394% BLUR AT HALF-THETA = 70 IS 9.82729% ENERGY = 88.3023% BLUR AT HALF-THETA = 75 IS 13.324% ENERGY = 93.3013% BLUR AT HALF-THETA = 80 IS 17.582% ENERGY = 96.9846% BLUR AT HALF-THETA = 85 IS 22.7296% ENERGY = 99.2404% BLUR AT HALF-THETA = 90 IS 28.9078% ENERGY = 100.% __________________________________________________________________________
TABLE 3 ______________________________________ ENERGY DENSITY INPUT HALF ANGLE: 50 DEGS; BLUR HALF ANGLE: 1.468028 DEGS; F LENGTH: 1.215706 ACTUAL HALF BLUR = 1.460521 ED WITHOUT INT. THETA/2 BLUR ED FILTER ______________________________________ 5 -.3556964 287.509 287.509 10 -.6825468 287.509 287.509 15 -.9513471 287.509 287.509 20 -1.132212 287.509 287.509 25 -1.19423 287.509 287.509 30 -1.1052 287.509 287.509 35 -.8314132 287.509 287.509 40 -.3374677 287.509 287.509 45 .413667 287.509 140.00 50 1.460521 287.509 70.00 55 2.842762 14.79476 7.00 60 4.600493 6.313195 1.22 65 6.773284 3.023969 0.24 70 9.398888 1.521802 0.03 75 12.51169 .770692 0.01 80 16.14093 .3740807 0.008 85 20.30903 .1578329 0.001 90 25.03012 3.807866E-02 0.00 ______________________________________
As in any lens, the set of parallel rays from an object at infinity are not all brought to a common focus point. Some of the incident rays will be brought to a relatively sharp focus at the detector while other rays will be spread out over a large blur circle as shown on FIG. 2.
In a conventional lens, the rays outside the selected bundle of rays, for example, from .theta.=60 degrees to .theta.=90 degrees can be removed by appropriately stopping down the lens. This cannot be done in the case of a lens-sphere because the corresponding parts of the lens are needed to collect rays from the other direction. However, the position of the detector (i.e., the focal point) can be chosen so that as many as possible of the incident rays fall within the desired resolution blur circle, which as discussed below may advantageously be about a 5 degree diameter. In accordance with the invention, about 60 percent of the total flux incident at the physical aperture of the system as defined by the actual outside diameter of the assembly is focused within the desired 5 degree blur circle. The target signal may be contaminated by generally low spatial frequency background clutter in some applications and by a strong adjacent point source, such as a flare, in other applications. The resulting detected image can be spatially filtered by well known digital processing techniques, for example in the digital domain after detection and digitization, to attenuate unwanted clutter-induced low spatial frequencies contributed by the extreme rays that cannot be focused to within the desired blur circle resolution. The disturbing effect of an adjacent strong point source is attenuated by the referenced interference filter which effectively limits the entrance aperture thereby reducing the percentage of energy in the out-of-focus blur spot.